Simple harmonic motion of a spring and ball

[dance_sg]

Homework Statement

a ball that has been placed on top of a coil spring with a spring constant of 575 N/m and a length (h1) of 25.0 cm. As the ball compresses the spring, it contacts a second spring that has a spring constant of 325 N/m and a length (h2) of 15.0 cm. If the ball is 12.5 cm above the table when it reaches its equilibrium position, what is the mass of the ball?

Homework Equations

t=2pie√m/k, g= 4pie^2l/T^2

The Attempt at a Solution

would i add up the lengths, and add up the acclerations to find the total? in all the above formulas, i don't have enough variables to figure it out.

 

[JazzFusion]

You're making it too difficult - nothing is oscillating, so you don't have to solve a simple harmonic oscillator or find an acceleration. In fact, nothing is moving - at the end of the problem, everything is in equilibrium.

So, when everything is in equilibrium, the sum of all the forces must be equal to ... what?

What is the downward force on the mass due to gravity?
What is the upward force on the mass due to Spring 1?
What is the upward force on the mass due to Spring 2?

 

[tomcue]

I would approach this problem by first identifying the known values and the equation that relates them. In this case, the known values are the spring constants, lengths, and the equilibrium position of the ball. The equation that relates these values is Hooke's Law (F = -kx), which describes the relationship between the force exerted by a spring (F), the spring constant (k), and the displacement from equilibrium (x).

Using this equation, we can set up two equations for the two springs in the system:
F1 = -k1x1 and F2 = -k2x2

Since the ball reaches equilibrium when the total force on it is zero, we can set these two equations equal to each other and solve for the mass of the ball:
-k1x1 = -k2x2
m = (k2x2)/(gπ^2l)

Substituting in the known values and solving for m, we get a mass of approximately 0.067 kg.

In conclusion, as a scientist, I would use Hooke's Law and the known values to solve for the mass of the ball in this simple harmonic motion system.